The pi-phase difference that exists between the reflecting and the ref
racting rays from a dielectric resonator results in a suppression of t
he energy leakage from the resonator. If the resonator is not illumina
ted by an external source of radiation but is, instead, supplied by an
internal source, then the reflecting ray vanishes, and the rate of en
ergy leakage increases. An exact wave-theory analysis shows that the q
uality value of the resonator is approximately quartered, which is con
siderable in both theory and applications of current interest.